The resistor-string (or resistor-ladder), which is usually composed of a number of series-connected resistors of equal value, is commonly used as a multiple reference voltages generator in an analog-to-digital circuits (ADC) or a digital-to-analog circuits (DAC). The resistance of each resistor in the resistor-string will not be a design value exactly when the resistor-string are fabricated in a silicon substrate. In other words, one can only expect the resistance of each resistor in the resistor-string could be very closer to each other, and they could never be the same due to the inherent limitation of the manufacturing process.
In the article "Trimless High Precision Ratioed Resistors in D/A and A/D Converters", published on IEEE Solid State Circuits Vol. 30, No. 8, August 1995, Wittman, Schardein, Hosticka, and Burbach, an application of a resistor-string in ADC or DAC is disclosed. In this article, the factors influencing the resistance value of each resistor during the manufacturing process are analyzed and verified. The article also disclosed a ladder-type resistor arranged in an intermeshed configuration so as to enhance the precision of the resistance value of each resistor.
U.S. Pat. No. 5,471,208 disclosed a circuit which automatically adjusts a resistor-string. A MOS is connected in parallel with a corresponding resistor. The resistance value of the MOS is adjusted, according to the comparison result of the voltage drop across the corresponding resistor with a reference voltage. As a result, the equivalent resistance of the MOS in parallel with the corresponding resistor is equal to a desired resistance value. In this way, the voltage drop across the corresponding resistor could be equal to the reference voltage.